Which of the following numbers is a multiple of 6? ${40,66,79,89,105}$
Answer: The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $40 \div 6 = 6\text{ R }4$ $66 \div 6 = 11$ $79 \div 6 = 13\text{ R }1$ $89 \div 6 = 14\text{ R }5$ $105 \div 6 = 17\text{ R }3$ The only answer choice that leaves no remainder after the division is $66$ $ 11$ $6$ $66$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $66$ $66 = 2\times3\times11 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $66$. We can say that $66$ is divisible by $6$.